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# Pro. Xuezhong SHI, College of Public Health

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Pro. Xuezhong SHI, College of Public Health

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【典型案例】 随机抽取15名健康成人,测定血液的凝血酶浓度(单位/毫升)及凝固时间,数据如表所示据此判断两项指标间有否相关? 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【案例解析】 实验设计类型：完全随机设计 研究目的：了解凝血时间与凝血酶浓度两个变量之间的关系 ——相关(correlation) ——回归(regression) 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
3.相关分析的分类 根据变量个数： 简单相关 simple correlation（直线相关 linear correlation) 偏相关 partial correlation : 在其它变量不变时，两个变量之间的关联性 根据数据的正态分布性： 参数分析方法 (Pearson) 非参数分析方法 (Spearman) 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Pearson积差相关系数 coefficient of product-moment correlation

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
（一）绘制散点图 图 凝血时间与凝血酶浓度散点图 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
（二）估计简单相关系数ρ 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
（三）相关系数ρ 的假设检验 由于抽样误差的存在，我们计算出来的样本相关系数未必等于总体相关系数，所以需要对相关系数进行假设检验。 若ρ≠0，说明X与Y之间有线性关系。 若ρ=0，说明X与Y之间无线性关系，但也可能存在其它相关关系。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
ρ的假设检验 H0: ρ=0 H1: ρ≠0 Sr 是ρ的估计值r 的标准误 查ν=n-2 的 t-分布表（附表2）。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【电脑实验】 数 据 录 入 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【结果解释】 结果表明，血液凝血酶浓度和凝固时间存在较强的负相关，相关系数为－0.926。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【小结】 1．样本的相关系数接近零并不意味着两变量间一定无相关性。只能说明两变量之间无线性相关关系，但还可能存在其他非线性关系。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【小结】 2．一个变量的值人为选定时莫作相关 药物的剂量一反应关系； 温度－细胞计数的关系； 因为剂量和温度不是随机变量。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【小结】 3．出现异常值时慎用相关。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【小结】 4. 相关未必真有内在联系。 如某农民喜得一贵子，于是在自家门前种了一棵小树留做纪念，结果发现：随着小树的逐渐长高，儿子的身高也在逐渐上长，于是他得出结论：儿子的身高与树高呈正相关。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【小结】 5. 分层资料盲目合并易出假象。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【典型案例】 例11-4 某地研究2 -7岁急性白血病患儿的血小板与出血症状程度之间的相关性，结果见表11-2，试进行相关分析。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【案例解析】 血小板出血症状程度是个等级资料，因此在进行相关分析时，不能用pearson相关 ，因为pearson相关 要求资料呈双变量正态分布。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【电脑实验】 数 据 录 入 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【结果解释】 结果表明，急性白血病患儿的血小板与出血症状程度无相关。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【典型案例】 例11-6 为观察婴儿腹泻是否与喂养方式有关，某医院儿科随机收集了消化不良的婴儿82例，把该院儿科所有消化不良的患儿视为一个总体的话，则该82例患儿可看作是一份随机样本。对每个个体分别观察腹泻与否和喂养方式两种属性，试分析两种属性的关联性。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
（一）计算列联系数 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
（二）列联系数的假设检验 等价于配对四格表关联性分析的卡方检验 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【电脑实验】 数 据 录 入 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
SPSS运算过程 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
SPSS运算过程 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
SPSS运算结果 列联系数的假设检验 列联系数 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【结果解释】 结果表明，婴儿腹泻与母亲喂养方式之间存在关联,其列联系数为0.329。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【电脑实验】 数 据 录 入 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
SPSS运算结果 列联系数 列联系数的假设检验 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【结果解释】 结果表明，甲状腺种类型与祖籍有关联,其列联系数为0.579。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【小结】 积差相关系数 定量变量 双变量正态分布 YES NO 秩相关系数 定性变量 列联系数 两变量关联性分析 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
Pearson积差相关系数 适用条件：双变量正态分布资料。 表示方法：r 注意事项：不可用相关系数检验所得P值的大小来判断有否线性关系。一定要先绘制散点图，看出两变量间有线性趋势时，再计算积差相关系数。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
Spearman秩相关 适用条件： —不满足正态分布的两变量随机样本 —等级资料 表示方法：rs 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Pearson积差相关和Spearman秩相关的主要联系

Dr. Xuezhong SHI, College of Public Heath
Pearson列联系数 适用条件:定性资料（一份随机样本，同时按两种属性分类）, 当两变量都是无序分类变量或一个是无序分类变量、另一个是有序分类变量时。 表示方法：r 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【案例讨论（一）】 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【案例解析】 Pearson 积差相关在对两定量变量间的相关性分析的实际问题中有广泛的应用，但应注意其适用条件，即双变量正态分布，例如这里的水质的碘含量是定量资料，是否正态分布权且不论，但甲状腺肿的患病率是属二项分布的分类资料，这显然不符合Pearson积差相关的条件，这份资料实际上该作Spearman等级相关。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【案例讨论（二）】 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【案例解析】 这里是三组独立样本的比较，据此不能考察关联性和计算关联系数。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【案例讨论（三）】 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【案例解析】 这里年龄和疗效都是有序变量，应当采用Spearman等级相关系数，而不应采用Pearson列联系数。 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
【最佳选择题】 1.积差相关系数的计算公式是_______。 A. B. C. D. 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
2. 相关系数的检验可用________。 A.散点图直接观察法代替 B. t检验 C. F检验 D. 卡方检验 E. 以上都可 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
3．计算积差相关系数要求________。 A. 因变量Y是正态变量，而自变量X可以不满足正态的要求 B. 自变量X是正态变量，而因变量Y可以不满足正态的要求 C. 两变量都要求满足正态分布规律 D. 两变量只要是测量指标就行 E. 因变量Y是定量指标，而自变量X可以是任何类型的数据 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
4 对两个分类变量的频数表资料作关联性分析，可用_______。 A. 积差相关 B. 秩相关 C. 列联系数 D. 线性相关 E. 等级相关 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath
5.对R×C列联表资料作频数分布的比较与作两变量关联性分析_______。 A.设计不同，统计量一样 B. 两者仅假设不同 C. 两者仅结论不同 D. 两者的P值不同 E. 两者检验水准不同 2017/3/9 Dr. Xuezhong SHI, College of Public Heath

Dr. Xuezhong SHI, College of Public Heath

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